com·po·si·tion / ˌkämpəˈzishən/ • n. 1. the nature of something's ingredients or constituents; the way in which a whole or mixture is made up: the social composition of villages. ∎ the action of putting things together; formation or construction. ∎ a thing composed of various elements. ∎ archaic mental constitution; character: persons who have a touch of madness in their composition. ∎ [often as adj.] a compound artificial substance, esp. one serving the purpose of a natural one: composition flooring. ∎ Linguistics the formation of words into a compound word. ∎ Math. the successive application of functions to a variable, the value of the first function being the argument of the second, and so on: composition of functions, when defined, is associative. ∎ Physics the process of finding the resultant of a number of forces. 2. a work of music, literature, or art. ∎ the action or art of producing such a work: the technical aspects of composition. ∎ an essay, esp. one written by a school or college student. ∎ the artistic arrangement of the parts of a picture. 3. the preparing of text for printing by setting up the characters in order. 4. a legal agreement to pay an amount of money in lieu of a larger debt or other obligation. ∎ an amount of money paid in this way. DERIVATIVES: com·po·si·tion·al / -shənl/ adj. com·po·si·tion·al·ly / -shənl-ē/ adv.
1. (relative product) A method of combining functions in a serial manner. The composition of two functions f : X → Y and g : Y → Z
is the function h : X → Z
with the property that h(x) = g(f(x))
This is usually written as g ◦ f. The process of performing composition is an operation between functions of suitable kinds. It is associative, and identity functions fulfill the role of units.
If R denotes the set of real numbers and f : R→R, f(x) = sin(x) g : R→R, g(x) = x2 + 3
then f ◦ g is the function h: h : R→R, h(x) = sin(x2 + 3)
The idea of composition of functions can be extended to functions of several variables.
2. A subdivision of a positive integer n into parts a1, a2,… ak in which the ordering is significant and in which n = a1 + a2 + … + ak
where each ai is a positive integer. It is thus similar to a partition (see covering) but in a partition the ordering is not significant. In general the number of compositions of n is 2n–1.
3. A particular form of association between entities found in object-oriented approaches. The association is used to indicate a hierarchy of objects such that objects lower in the hierarchy are part of objects higher in the hierarchy. Thus the hierarchy indicates a component structure.
1. The action, process, or art of composing especially pieces of music and works of literature.
2. An essay, usually short and written for training purposes, especially in school and usually in the English classroom.
3. A course in WRITING in a school or other educational institution.
4. The process of putting words and sentences together according to the traditional rules of GRAMMAR, STYLE, and RHETORIC.
5. An obsolete term for WORD-FORMATION.